Measurement of Branching-Fraction Ratios and CP Asymmetries in B^±→ D_CP±K^± Decays at Belle and Belle II

Abstract We report results from a study of B±→ DK± decays followed by D decaying to the CP-even final state K+K− and CP-odd final state $$ {K}_S^0{\pi}^0 $$ K S 0 π 0 , where D is an admixture of D0 and $$ {\overline{D}}^0 $$ D ¯ 0 states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle ϕ3. The results are based on a combined analysis of the final data set of 772 × 106$$ B\overline{B} $$ B B ¯ pairs collected by the Belle experiment and a data set of 198 × 106$$ B\overline{B} $$ B B ¯ pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be $$ \mathcal{A} $$ A CP+ = (+12.5 ± 5.8 ± 1.4)% and $$ \mathcal{A} $$ A CP− = (−16.7 ± 5.7 ± 0.6)%, and the ratios of branching fractions to be $$ \mathcal{R} $$ R CP+ = 1.164 ± 0.081 ± 0.036 and $$ \mathcal{R} $$ R CP− = 1.151 ± 0.074 ± 0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries $$ \mathcal{A} $$ A CP+ and $$ \mathcal{A} $$ A CP− have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5° < ϕ3 < 16.5°) or (84.5° < ϕ3 < 95.5°) or (163.3° < ϕ3 < 171.5°) and 0.321 < rB < 0.465.